The prior art is replete with finishing machines, including vibratory (the generic term) and vibrogyratory (a species thereof) finishing machines, of innumerable types and descriptions, most of which are adapted for the single stage surface finishing of a part of workpiece therein. When more than a single operation has been required or desired, this has ordinarily been effected by carrying out successive operations in a single machine, with the necessity of emptying the machine and replenishing the finishing medium therein with another type of finishing medium, or of using a series of machines, with necessary transfer from one machine to another and possible storage of partially finished parts or workpieces in between. A combination of fluid and solid finishing media has been employed by utilization of solid ceramic, plastic, or like abrasive media and at the same time spraying the finishing media and parts with various aqueous or chemical fluid surface finishing media, such as solvent wash, water rinse, rust preventive or inhibitor solutions, and the like, but such procedure does not provide the total surface finishing of a part or workpiece in the same manner as a succession of surface treatments of various types, particularly when it is desired or required that the part or workpiece have a highly polished surface which is entirely free of contaminants such as oils or greases and be completely dry. Proposals have been made for the successive finishing of parts or workpieces in a so-called horizontal Spiratron.TM. with baffles for transferring parts or workpieces from one section thereof to another section, containing different media and/or sprays, upon rotation of a finishing chamber, as in U.S. Pat. Nos. 3,074,068 and 3,073,080, but such devices are expensive and have not proved acceptable in practice. Neither have the multistage so called helical or vertical Spiratrons.TM. of U.S. Pat. No. Re. 27,084, for the same reasons. At the present stage of the development of this art, there is no satisfactory, economical, and practical vibratory or vibrogyratory finishing machine available to industry wherein parts or workpieces may be treated successively in a series of steps involving a plurality of solid or fluid surface treating media without the necessity of separating the partially-finished parts at an intermediate stage and transferring them to the next stage and perhaps storing them in between stages, and wherein parts or workpieces can be introduced into the vibratory finishing device and subjected to a plurality of surface treatments as desired, from beginning to end, and then exited from the finishing machine in a highly polished, uncontaminated, and dry state, ready for immediate use in applications requiring the most stringent specifications and tolerances, such as apply to roller bearings or the like. Neither has any suitable finishing trough or chamber been available for the employment in, on or in conjunction with a vibratory finishing machine for the accomplishment of such objectives. It is apparent that the finishing art, and industry in general which is highly reliant upon the same, would be greatly benefitted by the provision and availability of a new and improved finishing machine particularly adapted to multistage surface finishing operations, especially such a machine wherein the various stages or cycles of the surface finishing operation could be carried out in a single machine in a single pass or continuous manner, such as in a single continuous trough, especially such a trough which would be non-linear in nature to avoid inevitable conflicts with space and floor area limitations, as well as a novel method for the multistage surface finishing of parts or workpieces which would avoid the shortcomings of the prior art and present day equipment and practice.